OFFSET
1,3
COMMENTS
A multiset is normal if it spans an initial interval of positive integers. It is periodic if its multiplicities have a common divisor greater than 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
FORMULA
From Andrew Howroyd, Feb 04 2021: (Start)
G.f.: Sum_{d>=2} -mu(d)*x^d/((1 - x - x^d*(2-x))*(1-x)).
(End)
EXAMPLE
The a(5) = 13 periodic multisets:
(11), (22), (33), (44),
(111), (222), (333),
(1111), (1122), (1133), (2222), (2233),
(11111).
MATHEMATICA
allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];
Table[Length[Select[Union@@Rest/@Subsets/@allnorm[n], GCD@@Length/@Split[#]>1&]], {n, 10}]
PROG
(PARI) seq(n)=Vec(sum(d=2, n, -moebius(d)*x^d/(1 - x - x^d*(2-x)) + O(x*x^n))/(1-x), -n) \\ Andrew Howroyd, Feb 04 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2018
EXTENSIONS
a(12)-a(13) from Robert Price, Sep 15 2018
Terms a(14) and beyond from Andrew Howroyd, Feb 04 2021
STATUS
approved